Techniques will be developed for genetic analysis of complex diseases segregating in extended pedigrees of arbitrary structure. Diseases such as hypertension and psychiatric illness have both environmental and genetic components. However, identification of genes contributing to increased risk of such diseases has been limited by both computational and statistical constraints. The development of Markov Chain Monte Carlo (MCMC) methods have helped to overcome these limitations, providing information for gene localization, trait model estimation, haplotype analysis, and genetic map analyses, using data on extended pedigrees. The research now proposed is concerned with the extension of MCMC methods in several areas. We will develop improved methods for the MCMC analysis of gene descent in extended pedigrees, given data at multiple markers, using also sequential imputation and importance sampling Monte Carlo methods. The current approach to efficient MCMC sampling on pedigrees will be extended to allow explicit models for complex phenotypes to be included within Bayesian and likelihood-based joint segregation and multilocus linkage analyses. Where marker and phenotypic data are available on members of an extended pedigree, current methods will be extended to handle additional trait measures such as multivariate and ordered categorical phenotypes, to incorporate more complex patterns of censoring, and to allow for missing covariate information. We will develop measures of haplotype identity by descent (ibd) computationally and statistically well suited to linkage detection using data on extended pedigrees. We will compare the computational efficiency and statistical power of ibd-based linkage-detection methods with those of Bayesian and likelihood-based joint segregation and linkage analysis. We will develop MCMC methods for analysis of genetic map heterogeneity, genetic interference, and pedigree and genotyping errors, and assess the impact of these on the localization of genes contributing to complex traits. Methods will be evaluated by analyses on several simulated and real data sets, including pedigrees segregating cardiovascular disease or psychiatric disorders. These real data sets include several on which are available genome-wide marker screens or more localized multigene haplotypes. Finally, software will be developed that implements these methods, and will be documented and released for use by practitioners.